Table Of ContentHydraulic Design of
Labyrinth Weirs
HENRY T. FALVEY
ASCE
mess
American Society of Civil Engineers
1801 Alexander Bell Drive
Reston, Virginia 20191^400
Abstract: Hydraulic Design of Labyrinth Weirs is a comprehensive treatise on the hydraulic
design of labyrinth spillways. The book begins with a section on the theory of labyrinth
weirs and continues with detailed sections on significant factors that affect the discharge
characteristics such as crest shape, weir height, and sidewall angle. The design of a
labyrinth weir and modeling criteria is also covered. Several prototype labyrinth spillway
configurations are included as examples.
Library of Congress Cataloging-in-Publication Data
Falvey, Henry T.
Hydraulic design of labyrinth weirs / Henry T. Falvey
p. cm.
Includes bibliographical references and index.
ISBN 0-7844-0631-6
1. Labyrinth weirs—Design and construction. I. Title
IV. Title.
TC555 .F35 2002
627f. 883-dc21 2002027942
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Copyright © 2003 by the American Society of Civil Engineers. All Rights Reserved.
Manufactured in the United States of America.
Cover photo: Labyrinth weir, Tongue River Dam, Montana, USA. Photo by the author.
Preface
This book is the result of a demand for a comprehensive treatise on the hydraulic
design of labyrinth spillways. Both practicing engineers and researchers should find
the book useful in the hydraulic design of labyrinth weirs.
The book begins with a section on the theory of labyrinth weirs and continues with
detailed sections on significant factors that affect the discharge characteristics of
labyrinth weirs, such as crest shape, weir height, and sidewall angle. The most
common design curves are presented in Chapter 4. From these, a recommendation
was developed for a single design curve to be used in future designs. Chapter 7 is
devoted entirely to design, which should lead a designer to determine the optimum
configuration to meet specified hydrologic criteria. If the designer considers that the
configuration is sufficiently unique that a model study is required, Chapter 11 is
devoted to modeling criteria. Following these criteria will ensure that the model is
conducted in a manner that will provide accurate predictions of prototype
performance. To guide the designer, several prototype labyrinth spillway
configurations have been included as examples of what has been studied or installed
in the past.
During the preparation of this book, many long-held concepts were examined and
revised in an effort to clarify them. For instance, the idea of interference was
completely changed through the discovery of a paper that studied interference using
an entirely new approach. Similarly, a careful examination of the original paper on
nappe oscillation revealed that the problem was actually two separate problems that
need separate solutions. Finally, the definition of which head to use in the
computations was clarified.
The book would not have been possible without the input from many engineers and
consultants. Special thanks are extended to F. Lux; Aubian Engineering Inc.; J. Paul
Tullis; Utah State University; Kathy Frizell; the U.S. Bureau of Reclamation; Brian
Tracy; the Corps of Engineers; John J. Cassidy, Cassidy Consultants; Sal Todaro,
URS; and Michael Stevens, private consultant. Their helpful suggestions and input of
additional data were extremely beneficial in completing gaps in data and guiding the
direction of the book. I am grateful for the input from Professor Pinheiro on the unit
costs for specific features in the metric version of the Excel spreadsheet program, as
well as some of the photos of dams in Portugal. Professor Indlekofer was also a great
help in guiding my thoughts on interference.
iii
Nomenclature
A Area
A Contact Area
c
AI Coefficient for Tullis Curve
AI Coefficient for Tullis Curve
AS Coefficient for Tullis Curve
A4 Coefficient for Tullis Curve
AS Coefficient for Tullis Curve
B Length of Sidewall
B Batter on Sidewall
w
C(/) Disturbance Coefficient
C Discharge Coefficient with Interference
Ca Discharge Coefficient
Cd' Discharge Coefficient Referred to Conditions Upstream of Weir
Cds Downstream Saturation Level
Ck Discharge Coefficient from Kindsvater and Carter
C Mean value of Interference Effect
m
C Fusegate Discharge Coefficient
g
C Megalhaes Discharge Coefficient
p
C Reduced Discharge Coefficient
r
C Saturation concentration
s
C Upstream Saturation Level
u
CT Tullis Discharge Coefficient
C Darvas Discharge Coefficient
w
C Lux Discharge Coefficient
x
Ci Interference Coefficient
Ci Interference Coefficient
D Hydraulic Depth
D Depth of Cutoff Wall
c
D Depth of Sheet Pile Wall
s
D Throw Distance of Jet
t
E Efficiency of Air Entrainment
Ef Energy Flux
ET Efficiency of Air Entrainment at Any Temperature
Ew Total Energy at Any Point on Sill
£20 Efficiency of Air Entrainment at 20 degrees Celsius
Fb Free Board Distance
F Upstream Froude Number
us
Hb Jet Breakup Length
Hd Design Head
H Total Head Upstream of Weir
0
H L Piezometric Head of Lateral Flow Measured Relative to Invert
P
iv
H Total Head on Centerline of Channel
t
K Pressure Correction Factor
KI Crest Radius Coefficient
K2 Crest Radius Coefficient
L Length along Weir
La Length of Disturbance
Lde Effective Length of Distrubance
Ldim Ratio of Length to Upstream Head
L Equivalent Crest Length
e
M Apron Height
N Total Number of Flow Depth Measurements in Main Channel
P Weir Height
Q Discharge
Q Discharge over Side Weir
L
QN Discharge over an Equivalent Straight Weir
Qo Inflow Discharge
Q Submerged Discharge
s
R Radius of Crest
Rh Hydraulic Radius
S Depth of Weir in Flow Direction
S Gradient of Dissipated Energy
e
S Bottom Slope
0
Sf Friction Slope
T Free Surface Width
T Thickness of Cutoff Wall or Thickness of Floor Slab
s
T Thickness of Weir Wall
w
U Velocity of Lateral Flow
V Average Velocity of Main Flow
V Volume of Air Entrained
a
Vj Jet Velocity
V Upstream Velocity
us
V Axial Velocity Component (With Flow Direction)
x
V Normal Velocity Component (Perpendicular to Flow Direction)
y
W Width of One Cycle of Labyrinth Weir
W Width of Channel
c
X Crest Coordinate in Flow Direction
Y Crest Coordinate in Downward Vertical Direction
Y Upstream or Downstream Height of Apron
a
Z Crest Elevation
c
Z Upstream Water Surface Elevation
w
Z Reservoir Elevation
r
F Froude Number
W Weber Number
a Half Apex Width
g Gravitational Acceleration
V
h Depth of Flow over Crest
h Mean Depth of Flow over Weir
a
hd Submergence Depth
he Equivalent Head on Weir
h Measured Flow Depth over Crest
m
h Weir Head at Steady State
0
h Upstream Head on Weir Crest
u
k Bulk Liquid Film Coefficient
t
m Magnification
n Number of Labyrinth Cycles
q Lateral Flow Rate Per Unit Length Of Channel
r Aeration Deficit Ratio
rj Aeration Deficit Ratio at any Temperature
r2o Aeration Deficit Ratio at 20 degrees Celsius
t Time
t Time to Stabilize
s
t Bubble Contact Time
c
x Longitudinal Coordinate Along Channel Bottom Direction
y Coordinate Perpendicular To X On A Vertical Plane
a Sidewall Angle
otmax Maximum Sidewall Angle
a Velocity Distribution Factor
v
ad Aeration Deficit Ratio Constant
P Momentum Correction Factor
p Crest Pressure Coefficient
p
y Specific Weight Of Fluid
r\ Pressure Head Coefficient
6 Angle Between Channel Bottom And A Horizontal Plane
p Water Density
a Interfacial Surface Tension
TOS Boundary Shear Stress Along The X Direction
|i Magalhaes Discharge Coefficient
w
<|> Acute Angle between Channel Centerline and Weir Crest
<|) Angle between Lateral Flow Vector and Channel Centerline
c
AX Distance Between Stations
vi
Contents
Preface iii
Nomenclature iv
Chapter 1: Introduction 1
Purpose 1
Types of Spillways 1
Flow Characteristics 6
Other Purposes 6
Previous Installations 7
Chapter 2: Analytic Development 9
Approaches 9
Side Channel Spillways 9
Equations of Motion 9
Energy Equation 11
Momentum Equation 13
Discharge Coefficient 14
Skew Weirs 15
Labyrinth Weirs 16
Conclusions 16
Chapter 3: Nappe Interference 19
Introduction 19
Theory 20
Model Studies 24
Chapter 4: Crests Shapes 31
Types of Crests 31
Theoretical Minimum Value of the Discharge Coefficient 32
Discharge Characteristics 32
Sharp Crest and Flat Top Profile 32
Quarter-Round Profile 33
HalfnRound Profile 34
Nappe Profile or Ogee Crest Profile 37
ChapterS: Design Curves 41
Introduction 41
Basic Parameters 42
Definition of Upstream Head 43
Design Curves Derived from Model Studies 44
Taylor 44
vii
Darvas 47
Megalhaes and Lorena 49
Lux 50
Tullisetal. 53
Example Computations 54
From Hay and Taylor 55
From Darvas 55
From Megalhaes and Lorena 55
From Lux 55
From Tullis et al. 55
Critique of Design Curves 56
Chapter 6: Downstream Chute 61
Introduction 61
Supercritical Waves 61
Aprons 64
Submergence 67
Chapter 7: Nappe Oscillation 69
Introduction 69
Nappe Vibration 69
Case Study 70
Surging Flows 74
Conclusions 75
Chapter 8: Design 77
Significant Parameters 77
General Guidelines for Parameter Selection 77
Headwater Ratio 77
Vertical Aspect Ratio/Sidewall Angle 77
Magnification Ratio 78
Sidewall Angle/Magnification 78
Efficacy 79
Apex Ratio 81
Crest Shape 82
Interference Length Ratio 82
Approach Flow Conditions 82
Downstream Channel 84
Layout and Quantities 84
Dimensions 85
Quantities 86
Discharge Coefficient 87
Design Procedure 88
Steps 88
Spreadsheet 89
Chapter 9: Sedimentation and Ice 95
viii
Sedimentation Fundamentals 95
Boardman 96
Hellsgate 97
Garland Power Canal 98
Conclusions 100
Ice 100
Chapter 10: Aeration 103
Introduction 103
Theory 104
Falling Jet Types 104
Performance 106
Conclusions 107
Chapter 11: Special Cases 109
Introduction 109
Fusegates™ 109
Detention Dams 113
Sheet Piling 115
Chapter 12: Modeling Procedures 119
Introduction 119
Systematic Errors 119
Scale Effects Caused by Surface Tension 119
Method of Operation 121
Random Errors 123
Conclusions 124
Application 124
Case Study 125
Appendix A 131
Appendix B 145
Bibliography 149
Index 161
ix
